Feedback of passive systems: synthesis and analysis of linear robust control systems

The feedback interconnection of passive systems always leads to a stable control loop. This fact can be used for synthesis and analysis of linear robust control systems in a uniform framework. In the case of slowly varying uncertainties the plant can be represented by a linear time-invariant (LTI) multimodel. Rendering this multimodel passive and using a strong strictly passive controller ensures robust stability of the closed loop. The paper refines this idea to the design of robust observer-based controllers using parametric controller design. The new method allows the inclusion of a very extensive multimodel. Based on the well-accepted concept of pole assignment, the procedure yields robust controllers whose orders do not exceed the order of the plant. For rapidly varying uncertainties the plant must be modelled as a linear time-variant (LTV) system. To obtain an uncertain control loop that can also be analysed with the feedback theorem the LTV-components must be separated from the LTI system. It is shown that this can be done by establishing an affine relation between time varying parameters and the state-space matrices. The resulting closed-loop structure allows the application of the multivariable circle criterion which is used here in LMI form.